Order Of Operations

When solving expressions and equations we have to follow what we call the  "Order of Operations". These refer to grouping (parentheses), exponentiation, multiplication, division, subtraction and addition.

There is a Acronym to help remember the order of operations – PEMDAS. We also can use the phrase Please Excuse My Dear Aunt Sally.  This abbreviation helps us to remember what each letter stands for and the order in which the operations take precedence:

Parenthesis,
Exponents,
Multiplication,
Division,
Addition and
Subtraction.  

So we see that Parentheses outranks Exponents which outranks Multiplication and Division (these are in the same rank) and Addition and Subtraction (which are also in the same rank.)

For example, the expression

(3 – (4+13*(8+4/2))) would be worked out as follows.

Start with the innermost parentheses, (8+4/2). Division comes before addition, so first divide 4 by 2.         (8+2)

Now add       (10)

The expression is now (3 – (4+13*10))

Next comes the outer parentheses. The next highest ranking is exponents, so we square the 4, resulting in 16.

(3 – (16+13*10))

Next multiply    (3 – (16+130)

Add                 (3 – 146)

Subtract           -143, the answer.

Note:  If there are two order of operations that are in the same rank you always work from Left to Right.  For example:

                      3+4-5=
                          7-5= 2
You WOULD NOT subtract 4-5 first because it is out of the order since that is on the right side.  You ALWAYS work from Left to Right.  The same goes for multiplication and division. Always Left to Right!